Consider an object thrown into the air with an angle theta and initial velocity
ID: 2302143 • Letter: C
Question
Consider an object thrown into the air with an angle theta and initial velocity v theta. There is a strong air stream in the x direction, which produce the air resistance. The resistance force Fr is given as a function of the velocity of the object in x direction. Set up the equations of motion (i.e.,) for x and y direction. Here, you need to identify all the forces applied to the object during movement. When there is no air resistance (k= 0), find the equations for the location, x(t) and y(t), of the object as functions of time t, and gravitational constant g. Considering the air resistance (k=O), find the equations for the location, x(t) and y(t), of the object as functions of time t, object mass m, gravitational constant g, and air friction coefficient k Here, you will need to solve a differential equation to get the answer.Explanation / Answer
a)Forces alonmg x direction Fx=-kVx i
forces along y direction Fy=-mg j
b)x=V0Cos teta*t i
y=VSintetat- gt*t/2 j
c)y=VSintetat- gt*t/2 j
Fx=-kVx i
a=-(k/m)VCos teta
dv/dt=-(k/m)VCos teta
dv/v=-(k/m)Cos teta dt
ln v=-(k/m)Cos teta t
v=e^-(k/m)Cos teta*t
x=integral of e^(-(k/m)Cos teta*t )dt
x=-(m/k)e^(-(k/m)Cos teta*t )/costeta